The idea of exploiting quantum features of light to perform more precise astrophysical measurements is a long-desired goal of both the optics and astrophysics communities, but only recently have theoretical proposals started to be experimentally implemented. One important goal is to increase the baseline distance between telescopes in interferometry, and thus improve the angular resolution of the celestial object. Some of the earlier proposals rely on the use of quantum repeaters to connect the two baseline stations. However, another proposal employs other quantum optical approaches to circumvent the need for quantum repeaters, while still providing a quantum advantage. I will discuss the on-going project for building quantum-enhanced telescopes for precision astrometry, i.e., measurements of position and velocity of celestial objects. I will present a proof-of-principle experimental demonstration of a two-photon interferometer for such goal. Moreover, I will present a single-photon-sensitive spectrometer, based on a linear array of 512 single-photon avalanche diode detectors, with 0.04 nm spectral and 40 ps temporal resolutions. This device enables us to implement a spectral binning technique, essentially allowing us to perform multiple measurements together, because each frequency can be treated as an independent measurement. Such device could also be used in other applications. Lastly, I will report on our frequency-resolved Hanbury Brown-Twiss experiments. Our work represents an important step towards quantum telescopes.